> In a lottery, the more tickets you buy, the higher your chances to have the winning number.

Yes, and it's exactly the same in bitcoin with the hashing power. Each hash is a ticket.

> If we played with a roulette and said "the goal is to be the first to have a winning number at the roulette" and I can try 50 times before you start, obviously I am more likely to win our game, am I not?

In bitcoin the goal is not to be the first. The goal is to find a winning hash that's on a chain that will not be abandoned. As soon as a new block is propagated you start mining on the new head. It doesn't change anything that you previously worked on another chain. The time spent on the previous chain is not wasted, unless finding a block wouldn't have got you the reward.

There is a kind of a race if 2 blocks are found simultaneously. But that's not really what this discussion is about, and in this case the outcome depends mostly on network connectivity.